Two Stylized Facts and the GARCH (1,1) Model

Many high frequency economic or financial time series display two empirical characteristics: high kurtosis and positive autocorrelation in the centred and squared observations. The first-order autocorrelation is typically low, and the autocorrelation function decays slowly. These series are often modelled with a GARCH (1,1) model. In this paper it is shown why such a model with normal errors cannot adequately characterize these stylized facts. The same seems true for the IGARCH (1,1)model. It is also shown why one can improve the situation by replacing the normal error distribution by a leptokurtic one, although this may not provide a complete remedy